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Chapter 13

Chapter 13 . Risk-Adjusted Return on Capital Models. Definition of RAROC. RAROC = If RAROC > Hurdle rate then value adding. ROA = RORAC = EVA = economic value added = Adjusted income – ROE x K. Invest if  0. The Numerator: Adjusted Income. = Spread (direct income on loan) +

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Chapter 13

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  1. Chapter 13 Risk-Adjusted Return on Capital Models

  2. Definition of RAROC • RAROC = • If RAROC > Hurdle rate then value adding. • ROA = • RORAC = • EVA = economic value added = Adjusted income – ROE x K. Invest if  0. Saunders & Allen Chapter 13

  3. The Numerator: Adjusted Income • = Spread (direct income on loan) + • + Fees (directly attributable to loan) – • - Expected Loss (EDF x LGD) – • - Operating Costs (allocated to loan) • Then multiply the entire amount by 1 – the marginal tax rate. Saunders & Allen Chapter 13

  4. The Denominator: Capital at Risk • Market-based approach (BT model) • Measure the maximum adverse change in the market value of the loan resulting from an increase in the credit spread • Use duration model to measure price effects. • Experientially-based approach (BA model) • Calculate UL using a multiple x LGD x exposure x standard deviation of default rates. Saunders & Allen Chapter 13

  5. The Market-based Approach to Measuring Capital at Risk • If DL=2.7, L=$1m, R=1.1%, R=10%, then: L = -$ 27,000 Saunders & Allen Chapter 13

  6. Saunders & Allen Chapter 13

  7. The Experientially-based Approach to Capital at Risk Measurement • If 99.97% VAR (AA rating) and normal distribution, then the multiplier is 3.4. • But, most banks use a large multiplier because loan distributions are not normal. • BA uses multiplier = 6. • If LGD=.5, Exposure=$1m, Loan =.00225, then UL=6 x .00225 x .5 x $1m = $27,000 (same as market-based approach) Saunders & Allen Chapter 13

  8. Calculating the RAROC of the Loan Example • Spread = .2% x $1m = $2,000 • Fees = .15% x $1m = $1,500 • EL = .1% x $.5m = ($500) • Tax rate = 0% • Adjusted Income = $3,000 • RAROC = $3,000/$27,000 = 11.1% • If cost of capital < 11.1% then make loan. Saunders & Allen Chapter 13

  9. The RAROC Denominator and Correlations Saunders & Allen Chapter 13

  10. Incorporating Unsystematic Risk • Equation (13.18) is the traditional Sharpe ratio for a loan. But, if all idiosyncratic risk is diversified away, then no need for RAROC. RAROC deals with untraded and unhedgeable assets (loans). • Banks specialize in info-intensive relationship lending that cannot be hedged in capital markets. Risk of loan should be divided into: (1) liquid, hedgeable market risk component and (2) illiquid, unhedgeable component. • The correlation of the unhedgeable component with the bank’s portfolio will determine the loan’s price. So different banks (with different portfolio correlations) will have different pricing (credit risk). • Froot & Stein (1998): Loan’s hurdle rate =market price of the loan’s traded risk + bank shareholders’ cost of capital to cover nontradeable risk. The second term is idiosyncratic. Saunders & Allen Chapter 13

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